Question:medium
Match List I with List II:
List I List II A. Young’s Modulus II. $FL / [A(\Delta L)]$ B. Compressibility I. $(\Delta d / d) / (\Delta L / L)$ C. Bulk Modulus III. $- (1 / \Delta P)(\Delta V / V)$ D. Poisson’s Ratio IV. $- V \Delta P / \Delta V$
Match List I with List II:
| List I | List II |
|---|---|
| A. Young’s Modulus | II. $FL / [A(\Delta L)]$ |
| B. Compressibility | I. $(\Delta d / d) / (\Delta L / L)$ |
| C. Bulk Modulus | III. $- (1 / \Delta P)(\Delta V / V)$ |
| D. Poisson’s Ratio | IV. $- V \Delta P / \Delta V$ |
Show Hint
Remember that "Modulus" is always a measure of "Stiffness," while "Compressibility" is a measure of how "Squishy" a material is. They are inverses of each other!
Updated On: May 28, 2026
- A-II, B-III, C-IV, D-I
- A-III, B-II, C-I, D-IV
- A-II, B-IV, C-III, D-I
- A-IV, B-I, C-II, D-III
Show Solution
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Topic:
This question deals with the "Mechanical Properties of Solids." It focuses on the various elastic moduli and ratios that describe how materials deform under different types of external stress. Each modulus represents the ratio of a specific type of stress to its corresponding strain.
Step 2: Key Formulas and Approach:
The general definition of an elastic modulus is $\text{Stress} / \text{Strain}$.
Longitudinal Stress = $F/A$; Longitudinal Strain = $\Delta L / L$.
Volume Stress (Pressure) = $\Delta P$; Volume Strain = $\Delta V / V$.
Lateral Strain = $\Delta d / d$.
Step 3: Detailed Explanation:
Young's Modulus (A): This describes a material's resistance to change in length. It is the ratio of longitudinal stress ($F/A$) to longitudinal strain ($\Delta L/L$). Mathematically: $Y = \frac{F/A}{\Delta L/L} = \frac{FL}{A\Delta L}$. This matches with II.
Compressibility (B): Compressibility is defined as the reciprocal of the Bulk Modulus. It represents how easily a substance can be compressed. If Bulk Modulus is $B$, then Compressibility $K = 1/B = -\frac{1}{\Delta P} \frac{\Delta V}{V}$. This matches with III.
Bulk Modulus (C): This describes the material's resistance to a change in volume under uniform pressure. It is the ratio of hydraulic stress ($\Delta P$) to volumetric strain ($\Delta V/V$). Mathematically: $B = \frac{-\Delta P}{\Delta V/V} = -V \frac{\Delta P}{\Delta V}$. The negative sign indicates that an increase in pressure leads to a decrease in volume. This matches with IV.
Poisson's Ratio (D): This is not a modulus but a dimensionless ratio. It compares the lateral strain (change in diameter) to the longitudinal strain (change in length) when a rod is stretched. Mathematically: $\sigma = \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} = \frac{\Delta d/d}{\Delta L/L}$. This matches with I.
Step 4: Final Answer:
The correct matching sequence is A-II, B-III, C-IV, D-I.
This question deals with the "Mechanical Properties of Solids." It focuses on the various elastic moduli and ratios that describe how materials deform under different types of external stress. Each modulus represents the ratio of a specific type of stress to its corresponding strain.
Step 2: Key Formulas and Approach:
The general definition of an elastic modulus is $\text{Stress} / \text{Strain}$.
Longitudinal Stress = $F/A$; Longitudinal Strain = $\Delta L / L$.
Volume Stress (Pressure) = $\Delta P$; Volume Strain = $\Delta V / V$.
Lateral Strain = $\Delta d / d$.
Step 3: Detailed Explanation:
Young's Modulus (A): This describes a material's resistance to change in length. It is the ratio of longitudinal stress ($F/A$) to longitudinal strain ($\Delta L/L$). Mathematically: $Y = \frac{F/A}{\Delta L/L} = \frac{FL}{A\Delta L}$. This matches with II.
Compressibility (B): Compressibility is defined as the reciprocal of the Bulk Modulus. It represents how easily a substance can be compressed. If Bulk Modulus is $B$, then Compressibility $K = 1/B = -\frac{1}{\Delta P} \frac{\Delta V}{V}$. This matches with III.
Bulk Modulus (C): This describes the material's resistance to a change in volume under uniform pressure. It is the ratio of hydraulic stress ($\Delta P$) to volumetric strain ($\Delta V/V$). Mathematically: $B = \frac{-\Delta P}{\Delta V/V} = -V \frac{\Delta P}{\Delta V}$. The negative sign indicates that an increase in pressure leads to a decrease in volume. This matches with IV.
Poisson's Ratio (D): This is not a modulus but a dimensionless ratio. It compares the lateral strain (change in diameter) to the longitudinal strain (change in length) when a rod is stretched. Mathematically: $\sigma = \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}} = \frac{\Delta d/d}{\Delta L/L}$. This matches with I.
Step 4: Final Answer:
The correct matching sequence is A-II, B-III, C-IV, D-I.
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